Every formula
The whole corpus, searchable by name, by domain, or by the equation itself. Every one has its own page, its symbols, and a declared base dimension for each of them.
211 of 211
- Acoustic Impedance
Z = rho·vWaves - Adiabatic Process Pressure-Volume Relation
P2 = P1·(V1/V2)^gammaThermodynamics - Ampere-Maxwell Law
B_circ = μ0·(I + ε0·dΦE/dt)Electromagnetism - Angular Frequency From Period
ω = 2·π / TMechanics - Angular Frequency From Frequency
omega = 2·pi·fWaves - Angular Momentum (Point Mass)
L = m·v·rMechanics - Angular Velocity From Tangential Speed
ω = v / rMechanics - Average Power
P = W / tMechanics - Average Translational Kinetic Energy
KE = (3/2)·k_B·TThermodynamics - Beat Frequency
f_beat = abs(f1 - f2)Waves - Bernoulli Velocity From Pressure Drop
v2 = sqrt(2·(P1 - P2)/ρ + v1^2)Fluid dynamics - Bernoulli's Principle
P1 + (1/2)·ρ·v1^2 + ρ·g·h1 = P2 + (1/2)·ρ·v2^2 + ρ·g·h2Fluid dynamics - Biot-Savart Law (Long Wire)
B = μ0·I / (2·π·r)Electromagnetism - Bohr Energy Level
E = -2.1798723611·10^-18 / n^2Quantum - Bohr Orbit Radius
r = 5.29177210903·10^-11 · n^2Quantum - Boltzmann Entropy
S = kB·ln(Ω)Thermodynamics - Brewster's Angle
θ_B = atan(n2/n1)Optics - Buoyant Force (Archimedes)
F_b = ρ·g·VFluid dynamics - Capacitance Definition
C = Q / VElectromagnetism - Energy Stored in a Capacitor
U = (1/2)·C·V^2Electromagnetism - Capillary Rise Height
h = (2·γ·cos(θ)) / (ρ·g·r)Fluid dynamics - Carnot Efficiency
η_C = 1 - Tc/ThThermodynamics - Center of Mass (1D)
x_cm = Σ(m_i·x_i) / Σ(m_i)Mechanics - Centripetal Force
F_c = m·v^2/rMechanics - COP (Refrigerator)
COP_R = Q_c / WThermodynamics - COP (Heat Pump)
COP_HP = Q_h / WThermodynamics - Coefficient of Restitution (1D)
e = (v2p - v1p) / (v1 - v2)Mechanics - Combined Power of Thin Lenses in Contact
P = P1 + P2Optics - Compton Wavelength Shift
Δλ = (h / (m_e·c)) · (1 - cos(θ))Quantum - Continuity Equation (Incompressible Flow)
A1·v1 = A2·v2Fluid dynamics - Coulomb's Law
F = k·|q1·q2| / r^2Electromagnetism - Critical Angle (Total Internal Reflection)
θc = asin(n2 / n1), with n1 > n2 so the argument stays in [-1, 1]Optics - De Broglie Wavelength
λ = h / p = h / (m·v)Quantum - Decay Constant from Half-Life
lambda = ln(2) / t_halfNuclear - Mean Lifetime of a Decaying Nucleus
tau = 1 / lambdaNuclear - Diffraction Grating
d·sin(θ) = m·λOptics - Distance Modulus
μ = 5·log10(d) - 5Astrophysics - Doppler Effect (Sound)
f' = f·(c + v_r)/(c + v_s)Waves - Doppler Effect For A Moving Observer
f' = f·(v + v_o) / vWaves - Doppler Effect For A Moving Source
f' = f·v / (v - v_s)Waves - Quadratic Drag Force
Fd = (1/2)·ρ·Cd·A·v^2Fluid dynamics - Power Against Quadratic Drag
P = (1/2)·ρ·C_d·A·v^3Fluid dynamics - Drift Velocity of Charge Carriers
v_d = I / (n·A·e)Electromagnetism - Dynamic Pressure
q = (1/2)·ρ·v^2Fluid dynamics - Heat Engine Efficiency
η = W_out / Q_inThermodynamics - Elastic Collision 1D Final Velocity of Body 1
v1p = ((m1 - m2)·v1 + 2·m2·v2) / (m1 + m2)Mechanics - Elastic Collision 1D Final Velocity of Body 2
v2p = ((m2 - m1)·v2 + 2·m1·v1) / (m1 + m2)Mechanics - Elastic Potential Energy
U = (1 / 2)·k·x^2Mechanics - Electric Field of a Point Charge
E = k_e·Q / r^2Electromagnetism - Electric Potential Energy of a Charge Pair
U = k_e·q1·q2 / rElectromagnetism - Electric Potential of a Point Charge
V = k_e·Q / rElectromagnetism - Electric Power
P = V·IElectromagnetism - Electric Power (P = V^2/R)
P = V^2 / RElectromagnetism - Energy Density of an Electric Field
u = (1/2)·eps0·E^2Electromagnetism - Relativistic Energy-Momentum
E = sqrt((p·c)^2 + (m·c^2)^2)Relativity - Enthalpy
H = U + P·VThermodynamics - Entropy Change of an Ideal Gas (Isothermal)
dS = n·R·ln(V2/V1)Thermodynamics - Entropy Change (Reversible, Isothermal)
ΔS = Q / TThermodynamics - Escape Velocity
v = sqrt(2·G·M / r)Mechanics - Euler Equation (Ideal Fluid)
a = -gradP / ρFluid dynamics - Faraday Law
emf = -dΦB/dtElectromagnetism - First Law of Thermodynamics
dU = Q - WThermodynamics - Frequency From Period
f = 1 / TWaves - Gauss Law (Electric)
ΦE = Q / ε0Electromagnetism - Gauss Law (Magnetism)
ΦB = 0Electromagnetism - Gibbs Free Energy
G = H - T·SThermodynamics - Surface Gravitational Acceleration
g_surf = G·M / R^2Mechanics - Gravitational Potential Energy
U = m·g·hMechanics - Gravitational Potential Energy (General)
U = -(G·M·m) / rMechanics - Half-Life from Decay Constant
t_half = ln(2) / λNuclear - Heat Capacity Relation
Q = m·c·ΔTThermodynamics - Convective Heat Current (Newton's Law of Cooling)
dQdt = h·A·dTThermodynamics - Heisenberg Energy-Time Uncertainty
ΔE_min = hbar / (2·Δt)Quantum - Hooke's Law
F = -k·xMechanics - Hubble's Law (Recession Velocity)
v = H0·dAstrophysics - Hydrostatic Pressure
Δp = ρ·g·hFluid dynamics - Ideal Gas Internal Energy (Monatomic)
U = (3/2)·n·R·TThermodynamics - Ideal Gas Law
P·V = n·R·TThermodynamics - Ideal Transformer Ratios
Vp/Vs = Np/Ns and Ip/Is = Ns/NpElectromagnetism - Impulse-Momentum Theorem
J = F·ΔtMechanics - Energy Stored in an Inductor
U = (1/2)·Lind·I^2Electromagnetism - Point Source Intensity
I = P/(4·π·r^2)Waves - Kepler's Third Law (Orbital Period)
T = 2·π·sqrt(r^3 / (G·M))Mechanics - Kinematics (3D Position Vector)
r = (x, y, z)Mechanics - Kinematics (3D Velocity Squared)
v^2 = vx^2 + vy^2 + vz^2Mechanics - Kinematics (3D Velocity Vector)
v = (vx, vy, vz)Mechanics - Kinematics (Δx = ½(v+v₀)t)
Δx = (1/2)·(v_f + v_o)·tMechanics - Kinematics (Δx = v₀t + ½at²)
Δx = v_o·t + (1/2)·a·t^2Mechanics - Kinematics (v = v₀ + at)
v_f = v_o + a·tMechanics - Kinematics (v² = v₀² + 2aΔx)
v_f^2 = v_o^2 + 2·a·ΔxMechanics - Kinetic Energy
KE = 1/2·m·v^2Mechanics - Pressure from Kinetic Theory
P = (1/3)·ρ·v^2Thermodynamics - Latent Heat
Q = m·LThermodynamics - LC Resonant Frequency
f = 1 / (2·π·sqrt(Lind·C))Electromagnetism - Relativistic Length Contraction
L = L0 / γ, γ = 1/sqrt(1 - v^2/c^2)Relativity - Lens Power
P = 1 / fOptics - Lensmaker's Equation
1/f = (n - 1)·(1/R1 - 1/R2) => f = 1 / ((n - 1)·(1/R1 - 1/R2))Optics - Lorentz Factor
gamma = 1 / sqrt(1 - v^2/c^2)Relativity - Lorentz Force
F = q·(E + v·B)Electromagnetism - Mach Number
M = v / aFluid dynamics - Magnetic Field at the Center of a Current Loop
B = mu0·I / (2·R)Electromagnetism - Magnetic Field Inside a Solenoid
B = mu0·n·IElectromagnetism - Magnetic Flux Through a Surface
Phi = B·A·cos(theta)Electromagnetism - Magnetic Force on a Current-Carrying Wire
F = I·L·B·sin(theta)Electromagnetism - Lateral Magnification
M = -si / soOptics - Mass Defect
dm = (Z·m_p + Nn·m_n) - M_nucleusNuclear - Mass-Energy Equivalence
E = m·c^2Relativity - Mass Flow Rate
mdot = ρ·A·vFluid dynamics - Mean Molecular Speed
v_mean = sqrt(8·k_B·T / (pi·m))Thermodynamics - Mirror Equation (Image Distance)
1/f = 1/so + 1/si => si = 1 / (1/f - 1/so)Optics - Heat from Molar Heat Capacity
Q = n·C·dTThermodynamics - Moment Of Inertia Of A Point Mass
I = m·r^2Mechanics - Moment Of Inertia Of A Rod About Its Center
I = (1/12)·m·L^2Mechanics - Moment Of Inertia Of A Solid Disk
I = (1/2)·m·R^2Mechanics - Moment Of Inertia Of A Solid Sphere
I = (2/5)·m·R^2Mechanics - Linear Momentum
p = m·vMechanics - Most Probable Molecular Speed
v_p = sqrt(2·k_B·T / m)Thermodynamics - Motional EMF of a Moving Conductor
emf = B·L·vElectromagnetism - Newton's Second Law
F = m·aMechanics - Nuclear Binding Energy
BE = dm·c^2Nuclear - Ohm's Law
V = I·RElectromagnetism - Ohm's Law (Solve I)
I = V / RElectromagnetism - Ohm's Law (Solve R)
R = V / IElectromagnetism - Total Orbital Energy
E = -(G·M·m) / (2·r)Mechanics - Circular Orbital Velocity
v = sqrt(G·M / r)Mechanics - Torricelli Outflow Speed
v = sqrt(2·g·h)Fluid dynamics - Parallel Axis Theorem
I = I_cm + m·d^2Mechanics - Parallel Capacitance
C_total = Σ CiElectromagnetism - Parallel Inductance
1/L_total = Σ(1/Li)Electromagnetism - Parallel-Plate Capacitance
C = eps0·A / dElectromagnetism - Particle in a Box Energy
E = (n^2·h^2) / (8·m·L^2)Quantum - Pascal's Principle (Hydraulic)
F2 = F1·(A2/A1)Fluid dynamics - Simple Pendulum Frequency
f = (1 / (2·π))·sqrt(g / L), g = 9.80665 m/s^2Mechanics - Simple Pendulum Period
T = 2·π·sqrt(L/g)Mechanics - Perfectly Inelastic Collision Final Velocity
vf = (m1·v1 + m2·v2) / (m1 + m2)Mechanics - Photoelectric Effect
K_max = h·f - φQuantum - Photon Energy from Wavelength
E = h·c / λQuantum - Photon Momentum
p = h / λQuantum - Closed Pipe Harmonic Frequency
f = n·v / (4·L)Waves - Open Pipe Harmonic Frequency
f = n·v / (2·L)Waves - Planck–Einstein Relation
E = h·fQuantum - Laminar Pipe Flow (Poiseuille)
Q = π·r^4·Δp / (8·μ·L)Fluid dynamics - Poisson Equation (Gravity)
laplacian(φ) = 4·π·G·ρMechanics - Power Dissipated in a Resistor
P = I^2·RresElectromagnetism - Mechanical Power
P = W/t = F·vMechanics - Radiation Pressure
P_rad = I/cWaves - Poynting Vector
S = (E·B) / μ0Electromagnetism - Pressure
P = F/AMechanics - Projectile Maximum Height
H = (v0^2·sin(θ)^2) / (2·g)Mechanics - Projectile Range
R = (v0^2·sin(2·θ)) / gMechanics - Projectile Time of Flight
t = (2·v0·sin(θ)) / gMechanics - Radioactive Decay
N_t = N0·exp(-λ·t)Nuclear - Radioactive Activity
Act = lambda·NNuclear - Rayleigh Criterion (Angular Resolution)
θ = 1.22·λ / DOptics - RC Charging Voltage vs Time
V(t) = V0 · (1 - exp(-t/(R·C)))Electromagnetism - RC Circuit Time Constant
τ = R·CElectromagnetism - Reduced Mass
μ = (m1·m2) / (m1 + m2)Mechanics - Refractive Index from Speed
n = c/vOptics - Relativistic Doppler Effect (Longitudinal)
fp = f·sqrt((1 - beta) / (1 + beta))Relativity - Relativistic Kinetic Energy
KE = (1 / sqrt(1 - v^2/c^2) - 1)·m·c^2Relativity - Relativistic Momentum
p = m·v / sqrt(1 - v^2/c^2)Relativity - Relativistic Total Energy
E = m·c^2 / sqrt(1 - v^2/c^2)Relativity - Reynolds Number
Re = ρ·v·D / μFluid dynamics - RL Current Growth vs Time
i(t) = (V/R) · (1 - exp(-t·R/L))Electromagnetism - RMS Current from Peak Current
I_rms = I_peak / sqrt(2)Electromagnetism - Root-Mean-Square Molecular Speed
v_rms = sqrt(3·k_B·T / m)Thermodynamics - RMS Voltage from Peak Voltage
V_rms = V_peak / sqrt(2)Electromagnetism - Roche Limit (Rigid Body)
d = R·(2·rho_M / rho_m)^(1/3)Astrophysics - Rotational Kinetic Energy
KE = (1/2)·I·ω^2Mechanics - Newton's Second Law For Rotation
τ = I·αMechanics - Rydberg Wavelength
1 / λ = 1.0973731568·10^7 · (1/n1^2 - 1/n2^2)Quantum - Schrodinger Equation (Time-Dependent)
dpsi_dt = (-(hbar^2/(2·m))·laplacian_psi + V·psi) / hbarQuantum - Schwarzschild Radius
r_s = (2·G·M) / c^2Astrophysics - Series Capacitance
1/C_total = Σ(1/Ci)Electromagnetism - Series Inductance
L_total = Σ LiElectromagnetism - SHM Angular Frequency Of A Spring
ω = sqrt(k / m)Mechanics - SHM Frequency Of A Spring
f = (1 / (2·π))·sqrt(k / m)Mechanics - SHM Maximum Acceleration
a_max = ω^2·AMechanics - SHM Maximum Velocity
v_max = ω·AMechanics - SHM Period Of A Spring
T = 2·π·sqrt(m / k)Mechanics - SHM Total Energy
E = (1 / 2)·k·A^2Mechanics - Single-Slit First Minimum
a·sin(θ) = λ => θ = asin(λ / a)Optics - Snell's Law
n1·sin(θ1) = n2·sin(θ2)Waves - Sound Intensity Level (dB)
β = 10·log10(I/I0)Waves - Heat Capacity at Constant Pressure (Mayer's Relation)
Cp = Cv + n·RThermodynamics - Heat Capacity at Constant Volume (Monatomic)
Cv = (3/2)·n·RThermodynamics - Spherical Mirror Focal Length
f = R / 2Optics - Standing Wave Harmonic On A String
f = n·v / (2·L)Waves - Stefan–Boltzmann Law (Radiated Power)
P = ε·σ·A·T^4Thermodynamics - Stellar Luminosity (Blackbody)
L = 4·π·R^2·σ·T^4Astrophysics - Stokes Drag on Sphere
F_d = 6·π·μ·r·vFluid dynamics - Surface Tension Force
F = γ·LFluid dynamics - Terminal Velocity (Small Sphere, Stokes)
v_t = 2·(ρ_p - ρ_f)·g·r^2 / (9·μ)Fluid dynamics - Thermal Conduction (Steady State)
Qdot = k·A·ΔT / LThermodynamics - Linear Thermal Expansion
dL = alpha·L0·dTThermodynamics - Thin Lens Equation (Image Distance)
1/f = 1/so + 1/si => si = 1 / (1/f - 1/so)Optics - Relativistic Time Dilation
t = γ·t0, γ = 1/sqrt(1 - v^2/c^2)Relativity - Torque
τ = r·F·sin(θ)Mechanics - Uncertainty Principle
dp_min = hbar / (2·dx)Quantum - Newton's Law of Gravitation
F = G·m1·m2 / r^2Mechanics - Relativistic Velocity Addition
u = (u1 + u2) / (1 + (u1·u2)/c^2)Relativity - Volumetric Flow Rate
Q = A·vFluid dynamics - Wave Equation (1D)
u_tt = v^2·u_xxWaves - Wave Speed
v = f·λWaves - Wave Speed On A String
v = sqrt(T / mu)Waves - Wien Peak Photon Energy
E = 2.821·k_B·TQuantum - Wien's Displacement Law
λ_max = b / TThermodynamics - Work from Force and Displacement
W = F·s·cos(θ)Mechanics - Work-Energy Theorem
W = ΔKE = KE_f - KE_iMechanics - Work (Force · Displacement)
W = F·sMechanics - Work Moving a Charge Through a Potential Difference
W = q·dVElectromagnetism